J. Chem. Eng. Data 2007, 52, 687-690
687
Solubility of NaF in NaF + NaX + H2O (X ) ClO4 and NO3) Ternary Systems and Density and Refractive Index of the Saturated Solutions at 298.15 K Jaime W. Morales and He´ ctor R. Galleguillos* CICITEM, Departamento de Ingenierı´a Quı´mica, Universidad de Antofagasta, Chile
Felipe Herna´ ndez-Luis Departamento de Quı´mica-Fı´sica, Universidad de La Laguna, 38071 Laguna, Tenerife, Spain
Data on the solubilities of NaF were determined in NaF + NaClO4 + H2O and NaF + NaNO3 + H2O ternary systems, and the density and refractive index of the saturated solutions were measured at 298.15 K. The solubility data and physical properties were determined for different molalities of the second electrolyte present in the ternary systems, within a range of 0 to 1.0 mol‚kg-1. Experimental data on the density and refractive index were fit to polynomials as a function of NaClO4 or NaNO3 concentration. Finally, a thermodynamic description was made of the solid-liquid equilibrium for the two ternary systems, based on the Reilly, Wood, and Robinson (R-W-R) model for calculation of the mean ionic activity coefficient of NaF in the ternary saturated solution. The Bromley model was used for the calculation of the activity and osmotic coefficients of the binary systems because these are required for making calculations with the R-W-R model.
Introduction In a previous study,1 we presented experimental data on the activity coefficients of NaF in the NaF + NaClO4 + H2O ternary system at 298.15 K. As a continuation of studies of the properties of this system, the present study reports data on the solubility of NaF and the values of density and the refractive index of its saturated solutions. We also present the same experimental information for the NaF + NaNO3 + H2O system. Experimental data on solubility in these systems have not been found in the literature, despite the importance of this property for the design and simulation of crystallization operations. It is probable that these studies have not been carried out because the solubility of NaF gives values which are opposite to those shown by NaClO4 and NaNO3. These compounds are much more soluble than NaF. For example,2 at 293.15 K, the molality of saturation of NaF is 0.967 mol‚kg-1, whereas for NaClO4 and NaNO3, it is 14.8 mol‚kg-1 and 10.2 mol‚kg-1, respectively. In the present study, the experimental solubility data were correlated by following the procedures employed by Correa et al.3 These authors used the Reilly-Wood-Robinson model4 (R-W-R) to represent the solid-liquid equilibrium of various ternary systems. Following Correa et al., we used the Bromley5 model for calculation of the activity coefficients for binary systems containing these electrolytes because these values are required for studying ternary systems using the R-W-R model. Finally, experimental data on density and the refractive index were correlated using polynomial equations with five and four empirical coefficients, respectively.
Experimental Section Materials. Analytical-grade sodium fluoride, sodium perchlorate monohydrate, and sodium nitrate were supplied by * Corresponding author. E-mail:
[email protected]. Fax: 56-55240152.
Merck with minimum purities of 99 %, 99 %, and 99.5 %, respectively. All of the chemicals in this study were used without further purification. NaF and NaNO3 were dried to constant weight for 48 h at 373.15 K prior to use. NaClO4‚H2O was maintained in a desiccator, at ambient temperature, for 24 h prior to its use. The water employed in all the experiments was distilled and deionized (conductivity < 0.5 µS·cm-1) before use. Apparatus and Procedures. Known masses of water, NaClO4 (or NaNO3), and NaF, the latter being in excess to ensure saturation of the solutions, were measured on a Mettler-Toledo model AX204 analytical balance with a precision of 0.07 mg. A rotary, thermostatically controlled water bath with a holder containing twelve 20 mL glass jars was used to obtain data on the phase equilibria. The system worked at 298.15 K, with an accuracy of 0.1 K. The samples were stirred for 72 h to reach equilibrium at the desired temperature. In all cases, the experiments were performed in duplicate. Following the agitation step, samples were allowed to decant for a further period of 4 h at constant temperature. The clear liquid of each equilibrium solution was collected by syringe and filtered using an Acrodisc 25 mm syringe filter, with a nominal pore size of 45 µm, for subsequent determinations of concentration, density, and refractive index. Syringes and other apparatuses used in the procedure were maintained at slightly elevated temperature to avoid any tendency of precipitation of salts from the solutions under study due to a decrease in temperature. The content of fluoride in the ternary systems was obtained by an ion-selective electrode method (4500-F- method6) using a Fischer Scientific accumet model 25 pH/ion meter and a VWR Scientific fluoride electrode (catalog number 34105-106). Samples for chemical analysis of approximately 4.0 g were diluted in a volume of 250 mL with deionized water having a conductivity of 0.5 µS·cm-1. Respective dilutions were then made such that a calibration line could be obtained. The calibration line was obtained using aqueous solutions of F- from 0.5 to 2
10.1021/je060220d CCC: $37.00 © 2007 American Chemical Society Published on Web 03/03/2007
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Table 1. Solubility of NaF (S), Density (G), and Refractive Index (nD) in NaF + NaX + H2O (X ) ClO4 or NO3) Ternary Systems at 298.15 K m2
S
F
mol‚kg-1
mol‚kg-1
g‚cm-3
0.0000 0.1145 0.2285 0.3420 0.4550 0.5677 0.6798 0.7916 0.9028 1.0136
m2
S
F
mol‚kg-1
mol‚kg-1
g‚cm-3
nD
NaF(1) + NaClO4(2) + H2O(3) 0.982 1.03790 0.904 1.04457 0.826 1.05154 0.775 1.05875 0.717 1.06568 0.646 1.07452 0.580 1.08227 0.534 1.09080 0.493 1.10045 0.441 1.10974
1.3374 1.3380 1.3386 1.3392 1.3398 1.3405 1.3412 1.3419 1.3427 1.3436
NaF(1) + NaNO3(2) + H2O(3) 0.982 1.03790 0.943 1.04148 0.890 1.04503 0.849 1.04852 0.802 1.05249 0.766 1.05615 0.733 1.05987 0.712 1.06371 0.674 1.06766 0.652 1.07152 0.614 1.07540
0.0000 0.1000 0.2001 0.2999 0.3999 0.5000 0.6000 0.6999 0.7997 0.8999 0.9999
nD
1.3374 1.3375 1.3381 1.3388 1.3394 1.3401 1.3408 1.3414 1.3421 1.3427 1.3434
Table 2. Values for Coefficients in Equations 1 and 2 system
βI1
βI2
βI3
βI4
βI5
NaF(1) + NaClO4(2) + H2O(3) NaF(1) + NaNO3(2) + H2O(3)
1.03786 1.03789
0.06002 0.03623
-0.00701 -0.00519
0.03052 0.01480
-0.01282 -0.00844
βII2
βII3
βII4
-0.00042 0.00530
0.00123 -0.00261
density
system
βII1
NaF(1) + NaClO4(2) + H2O(3) NaF(1) + NaNO3(2) + H2O(3)
1.3374 1.3374
refractive index
ppm. The solubility values of the ternary systems represent the means of two independent replicates. On the basis of the preceding, the uncertainty was ( 0.029 g of NaF/100 g of solution (( 0.007 mol·kg-1) for the NaF + NaClO4 + H2O system and ( 0.013 g of NaF/100 g of solution (( 0.003 mol·kg-1) for the NaF + NaNO3 + H2O system. The NaF concentration in the binary system (NaF + H2O) was determined by evaporation of known masses of filtered saturated solutions at 393.15 K. Taking into account that the experiments were carried out in duplicate, the uncertainty was ( 0.01 g of NaF/100 g of solution. Density measurements were carried out in triplicate using a Mettler-Toledo model DE50 oscillation densimeter, with a resolution of ( 1 × 10-5 g·cm-3. The temperature was thermostatically controlled to 298.15 ( 0.1 K by means of a self-contained Peltier system provided with the densimeter. Density values represent the average of two independent experiments, with the measured values being reproducible to within ( 8 × 10-5 g·cm-3. The refractive index of each solution was determined using a Mettler-Toledo model RE40 refractometer with a resolution of ( 1 × 10-4. The measurements were repeated at least three times with no appreciable variation. As in the case of the densimeter, the refractometer temperature was controlled to 298.15 ( 0.1 K by a self-contained Peltier system. Refractive index values represent the average of two independent experiments, with the measured values being reproducible to within ( 1 × 10-4.
Results and Discussion Solubility. Table 1 shows the solubility values of NaF (S) expressed as molality for both ternary systems evaluated in this study. It is observed that in both systems the solubility of NaF decreases with the molality of the second electrolyte (m2) present in the system. In the NaF + NaClO4 + H2O system, the solubility decreases from 0.982 mol‚kg-1 in a solution without NaClO4 to 0.441 mol‚kg-1 when the NaClO4 reaches a molality of approximately 1.0 mol‚kg-1. However, in the NaF + NaNO3 + H2O system, the interval of decrease in the solubility is less,
0.00527 0.00330
going from 0.982 mol‚kg-1 (solution without NaNO3) to 0.614 mol‚kg-1 when the NaNO3 has a molality of approximately 1.0 mol‚kg-1. The decrease in the solubility of NaF can be explained by the common ion effect. The contribution of sodium ions to the system by NaClO4 or NaNO3 tends to set back the dissociation equilibrium of the salt; that is, it is displaced more toward the formation of NaF than to its dissociation into F- and Na+ ions, and therefore the solubility of the salt decreases. On the basis of the experimental results, this effect is greater when NaClO4 is present. The solubility of NaF in water in this study (0.982 mol‚kg-1) is near the values given in the literature. Linke and Seidell7 reported that at 25 °C the value was 3.98 g of NaF/100 g of solution, representing a molality of 0.987 mol‚kg-1. Recently, Aghaie and Samaie8 reported a value of 0.973 mol‚L-1. Converting our experimental datum to molarity, using the corresponding density value from Table 1, we obtained 0.979 mol‚L-1. Physical Properties. Table 1 also presents experimental density values (F) and the refractive index (nD) of the saturated solutions of the systems studied. For density, with a constant value for m2, it can be noted that the density values of the NaF + NaClO4 + H2O system are always greater than those of the NaF + NaNO3 + H2O system. This indicates that the total mass of the dissolved salt in the first system is larger. For example, when NaClO4 has an m2 value of 0.9 mol‚kg-1 (equal to 110.2 g of NaClO4/1000 g of H2O), the solubility of NaF is 0.493 mol‚kg-1 (equal to 20.7 g of NaF/1000 g of H2O), which leads to a value of 130.9 g of salt/1000 g of H2O. When the molality of NaNO3 is 0.9 mol‚kg (76.5 g of NaNO3/1000 g of H2O), the solubility of NaF is 0.65 mol‚kg-1 (27.3 g of NaF/1000 g of H2O), which leads to a value of only 103.8 g of salt/1000 g of H2O. Table 1 shows that the values for the refractive index of both systems are not markedly different. For m2 less than 0.45 mol‚kg-1, the system containing NaClO4 shows greater nD values; however, beginning from this value of m2, both systems tend to have similar values for nD.
Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007 689 Table 3. Ion-Interaction Parameters of the R-W-R Model at 298.15 K system NaF(1) + NaClO4(2) + H2O(3) NaF(1) + NaNO3(2) + H2O(3)
Figure 1. Density as a function of the molality of NaClO4 or NaNO3 at 298.15 K. Experimental points: 2, NaF + NaNO3 + H2O system; b, NaF + NaClO4 + H2O system; s, calculated from eq 1.
The values for the density and refractive index at saturation were correlated as a function of the molality of the second electrolyte (m2) present in the system (NaClO4 or NaNO3), following eqs 1 and 2 F (g/cm3) ) βI1 + βI2m2 + βI3m22 + βI4m32 + βI5m42
(1)
nD ) βII1 + βII2 m2 + βII3 m22 + βII4 m32
(2)
where βji are empirical coefficients. The optimized values of these coefficients are given in Table 2. The average absolute deviation (AAD) between the experimental density values and those calculated using eq 1 is 1.7 × 10-4 g‚cm-3 for the first ternary system (NaF + NaClO4 + H2O) and 4.7 × 10-5 g‚cm-3 for the second ternary system (NaF + NaClO4 + H2O). For the refractive index, both systems have an AAD value of 1 × 10-4. These results confirm the good fit of the experimental data to the physical properties studied. Figure 1 presents a comparison between the experimental density values and those calculated using eq 1. Thermodynamic Representation of the Solid-Liquid Equilibrium. The solid-liquid equilibrium of the two ternary systems at 298.15 K was analyzed following the procedure described by Correa et al.3 These authors successfully applied the ReillyWood-Robinson4 and the Bromley5 models to correlete the solubility data of four ternary systems having a common ion. All the systems were analyzed at 298.15 K, and the electrolytes were of the 1:1 type. In the thermodynamic analysis of the present study, the R-W-R model permits estimation of the activity coefficient of NaF in the ternary system, whereas the Bromley model is used for calculating the activity coefficient of the NaF + H2O system and the osmotic coefficients of the NaF + H2O, NaClO4 + H2O, and NaNO3 + H2O binary systems. For systems of two 1:1 electrolytes, with a common ion, saturated with respect to component 1, and without forming hydrates, the solubility product (Kps) is given by Kps ) (m/1 γ/1)2 ) m1(m1 + m2)γ21 m/1
γ/1
(3)
where and are the molality and mean ionic activity coefficient of component 1 in the binary saturated system and m1, m2, and γ1 are the molalities of components 1 and 2 and the mean ionic activity coefficient of component 1 in the ternary system.
E
F
AAD
kg‚mol-1
kg2‚mol-2
mol‚kg-1
0.29687 0.17293
-0.01732 -0.12953
0.005 0.004
Following eq 3, the value of Kps can be obtained starting from the information from a saturated binary solution, which in this case has a value of 0.318. For this estimation, we assume that the experimental value of m/1 is 0.982 mol‚kg-1 (obtained from Table 1), and for this concentration, γ/1 has a value of 0.574, determined from the Bromley5 model using BNaF ) 0.0041 kg‚mol-1. For a fixed temperature, the solubility of NaF in the ternary system (m1) can be calculated from eq 3, given the Kps and the mean ionic activity coefficient of NaF in the ternary system (γ1). In this way, the description of the solubility of NaF can be provided as a function of the molality of the second electrolyte present in the ternary system (m2). The R-W-R model was used to calculate γ1, the expression of which for ternary systems with a common ion and 1:1 electrolytes is given by3 ln γ1 ) ln γ01 + Y2(φ02 - φ01) + Y2m[E + 0.5(1 + Y1)Fm]
(4)
where γ1 and γ01 are the mean ionic activity coefficients of NaF in the ternary solution at its molality m1 and in the binary solution at a total molality m, respectively, where m ) m1 + m2. The symbols φ01 and φ02 represent the osmotic coefficients of the binary solutions of NaF and the second electrolyte (NaClO4 or NaNO3), respectively, evaluated at a total molality m. Y1 and Y2 are the molar fractions (free of water) of the NaF and the second electrolyte in the ternary solution (NaClO4 or NaNO3). E and F are parameters of the mixture, which are related to the interactions of the different ions but are equal in charge. In this case, this is represented by the interactions F-ClO4 (for the NaF + NaClO4 + H2O system) and F-NO3 (for the NaF + NaNO3 + H2O system). The values of γ01, φ01, and φ02 are determined using the Bromley model. The advantage of this model is that it requires the use of only one parameter, symbolized by B. For 1:1 electrolytes at a temperature of 25 °C, these expressions are given by5 ln γ01 ) 2.303
[
-0.511m1/2 (0.06 + 0.6B1)m + + B1m 1 + m1/2 (1 + 1.5m)2
1 - φ0i ) 2.303 ×
[
]
(5)
]
0.511P(m1/2) - (0.06 + 0.6Bi)0.5mR(1.5m) - 0.5Bim (6) m
where i ) 1, 2 (1 ) NaF, 2 ) NaClO4 or NaNO3) P(m1/2) ) (1 + m1/2) R(1.5m) )
[
1 - 2 ln(1 + m1/2) (1 + m1/2)
]
ln(1 + 1.5m) 1 + 3m 2 1.5m (1 + 1.5m)2 1.5m
(7)
(8)
With eq 3 and the knowledge of parameters E and F (eq 4), we can predict the solubility values; nevertheless, these are unknown and will be determined using experimental information produced in this study. Thus, the correlation of the experimental
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Journal of Chemical and Engineering Data, Vol. 52, No. 3, 2007
Conclusions
Figure 2. Solubility of NaF as a function of the molality of NaClO4 or NaNO3 at 298.15 K. Experimental points: 2, NaF + NaNO3 + H2O system; b, NaF + NaClO4 + H2O system; s, calculated from eqs 3 and 4.
solubility data is carried out using the following iterative procedure: for a given experimental value of m2 (NaClO4 or NaNO3), one finds the value of m1 and the values of parameters E and F which permit the simultaneous solutions of eqs 3 and 4. In the iterative process for electrolytes NaClO4 and NaNO3, the values for the B parameter used were5 0.0330 kg‚mol-1 and -0.0128 kg‚mol-1, respectively. The value of this parameter for NaF has been presented in the preceding paragraph as 0.0041 kg‚mol-1. The values of parameters E and F obtained from the iteration for the ternary systems are shown in Table 3. In this table are also included the AADs between the experimental solubility values and those estimated by the iteration process. Figure 2 shows in graphic form the good agreement existing between the experimental and the calculated values for different concentrations of the second electrolyte present in the system (m2). Supposing that the values of the parameters B, E, and F remain constant with temperature, it would be possible to predict the solubility values at other temperatures, following the procedures given in this study. To carry out such a prediction for a given temperature, we must know the solubility of the NaF + H2O system to then estimate the Kps. If we do not have this information, the Kps can be estimated using the van’t Hoff equation. This type of prediction is useful in the design and operation of crystallizers; nevertheless, it is only possible to carry out for temperatures near 298.15 K because the parameters of the models are temperature dependent.
Data are presented on the solubility of NaF, at 298.15 K, for the NaF + NaClO4 + H2O and NaF + NaNO3 + H2O systems. The results showed that the increase in the concentration of the NaClO4 or NaNO3 produced a decrease in the solubility of NaF. It is concluded that this behavior was a consequence of the common ion effect. It was shown that the Reilly-WoodRobinson and Bromley thermodynamic models were good alternatives for representing the solid-liquid equilibria of both ternary systems. We also presented data on the density (F) and refractive index (nD) of the saturated solutions at 298.15 K. The results showed that both properties increased with increases in the concentrations of NaClO4 or NaNO3 in the system, and the values could be represented using a polynomial as a function of the concentration of NaClO4 or NaNO3. In general, the values of nD in both ternary systems are similar; nevertheless, the values of F in the NaF + NaClO4 + H2O system are greater than those of the NaF + NaNO3 + H2O system. This indicated that the total mass of dissolved salts was greater in the first system.
Literature Cited (1) Herna´ndez-Luis, F.; Benjumea, D.; Va´zquez, M.; Galleguillos, H. Activity Measurements in the NaF + NaClO4 + H2O Ternary System at 298.15 K. Fluid Phase Equilib. 2005, 235, 72-82. (2) Dean, J. D. Lange’s Handbook of Chemistry, 40th ed.; McGraw-Hill: New York, 1992. (3) Correa, H.; Vega, R.; Flores, F. Equilibrio So´lido-Lı´quido en Soluciones Acuosas de Electrolitos Fuertes. I. Uso de Modelos de ReillyWood-Robinson y de Bromley. Contrib. Cient. Tecnol. 1980, 44, 5-13. (4) Reilly, P. J.; Wood, R. H.; Robinson, R. A. The Prediction of Osmotic and Activity Coefficients in Mixed-Electrolyte Solutions. J. Phys. Chem. 1971, 75, 1305-1315. (5) Bromley, L. A. Thermodynamics Properties of Strong Electrolytes in Aqueous Solutions. AIChE J. 1973, 19, 313-320. (6) Standard Methods for the Examination of Water and Wastewater, 19th ed.; Prepared and Published Jointly by American Public Health Association, American Water Works Association, and Water Environment Federation: Washington, DC, 1995. (7) Linke, W. F.; Seidell, A. Solubilities of Inorganic and Metal Organic Compounds; American Chemical Society: Washington ,DC, 1965. (8) Aghaie, M.; Samaie, E. Non-ideality and Ion-paring in Saturated Aqueous Solution of Sodium Fluoride at 25 °C. J. Mol. Liq. 2006, 126, 72-74.
Received for review May 16, 2006. Accepted January 20, 2007.
JE060220D
